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Solve for y 1/(y^2)=1/(2y^2)+(y-5)/(2y^2)
Step 1
Find the
LCD
of the
terms
in the
equation
.
Finding the
LCD
of a list of values is the same as finding the
LCM
of the
denominators
of those values.
Since contains both numbers and
variables
, there are two steps to find the
LCM
. Find
LCM
for the
numeric
part then find
LCM
for the
variable
part .
The
LCM
is the smallest
positive number
that all of the numbers
divide
into evenly.
1. List the
prime
factors
of each number.
2.
Multiply
each
factor
the greatest number of times it occurs in either number.
The number is not a
prime
number because it only has one positive
factor
, which is itself.
Not
prime
Since has no
factors
besides and .
is a
prime
number
The
LCM
of is the result of multiplying all
prime
factors
the greatest number of times they occur in either number.
The
factors
for are , which is multiplied by each other times.
occurs times.
The
LCM
of is the result of multiplying all
prime
factors
the greatest number of times they occur in either
term
.
Multiply
by .
The
LCM
for is the
numeric
part multiplied by the
variable
part.
Step 2
Multiply
each
term
in by to
eliminate
the
fractions
.
Multiply
each
term
in by .
Simplify the left side.
Rewrite using the
commutative property of multiplication
.
Combine
and .
Cancel the
common factor
of .
Cancel the
common factor
.
Rewrite the
expression
.
Simplify the right side.
Simplify each
term
.
Rewrite using the
commutative property of multiplication
.
Cancel the
common factor
of .
Factor
out of .
Cancel the
common factor
.
Rewrite the
expression
.
Cancel the
common factor
of .
Cancel the
common factor
.
Rewrite the
expression
.
Rewrite using the
commutative property of multiplication
.
Cancel the
common factor
of .
Factor
out of .
Cancel the
common factor
.
Rewrite the
expression
.
Cancel the
common factor
of .
Cancel the
common factor
.
Rewrite the
expression
.
Subtract from .
Step 3
Solve the
equation
.
Rewrite the
equation
as .
Move all
terms
not containing to the right side of the
equation
.
Add to both sides of the
equation
.
Add and .
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